This invention is in the field of electrical communications and relates to data processing systems having an internal program element and which represent numerical information by electromagnetic radiation of optical wavelengths, and more particularly to such systems as may be applied to pattern recognition.
In early optical computers, input numerical quantities were represented by the optical transmission at one particular point on a photographic transparency and the results were represented by the optical intensities of light rays. When a ray passed through a point on the transparency, an attenuation occurred that provided a multiplication of the quantity represented by the ray and when several rays converged to a point the intensities combined linearly to provide an additive capability. An account of these "incoherent" optical computers has been given by B. J. Howell, Jour. Optical Soc. Am., Vol. 49, No. 10, p. 1012, October 1959. A typical device of this type is Berger's cross-correlator, U.S. Pat. No. 2,787,188. In Berger's invention, the input variables are the values of the functions to be correlated and the output result is the cross-correlation function; each value of this function being a (different) function of the input variables. These many output numerical values are computed simultaneously (in parallel) from the input data by rays passing through the input transparencies. This parallelism gives these simple inexpensive computing devices a very high data processing rate.
Berger's correlator directed a ray only once through the input transparency and hence was limited to output results linear in the input variables. By making both transparencies represent the same function, it computes the auto-correlation function which is non-linear in the input since it contains products and powers of the values of the input function, i.e., products and powers of the input variables. To eliminate the inconvenience of providing two copies of the same input function, L. Kovasynay and A. Arman, Rev. Sci. Instr., Vol. 28, p. 793, October 1957, showed how suitably located mirrors could be used to redirect the rays so that they passed twice through a single input transparency to produce the auto-correlation function. By redirecting the rays through optical fibers to repeated passage through the input transparency, Gamba, U.S. Pat. No. 3,323,407, constructed a computing device which evaluates more general non-linear polynomial functions of the input. A disadvantage of that technique is that the coefficients of the polynomials could not be controlled, but were necessarily random; however, Gamba showed the even then polynomial functions could be very useful as discriminant functions in pattern recognition. (When an image or pattern is represented by, possibly many, numerical quantities certain functions of these variables, called discriminant functions, indicate the presence of certain key features in the pattern when the values of the functions exceed certain thresholds.)
The incoherent optical computers that use intensities to represent numerical quantities are limited to positive values since intensities cannot be negative. In the 1950's, it was recognized that numbers could be represented by the complex amplitudes of the rays, and by the complex transmissions of transparencies. This allowed negative numbers to be handled. When coherent light is used, amplitudes combine linearly to provide the additive capability. By taking advantage of the Fourier transforming property of a lens, a spatial filtering can be performed in this way which is equivalent to a cross-correlation with negative or complex coefficients, e.g., see C. O. Carlson, U.S. Pat. No. 3,085,469.
In early coherent optical computers, a difficulty was found in adjusting the argument of the complex transmission of the transparencies since variations in the index of refraction of the supporting substrate, film or glass plate, also influenced the phase of the transmitted wave. This difficulty was overcome by the introduction of holographic methods. In holography, a data value (or image point) is recorded as a widely dispersed holographic element (e.g., a photographic "diffraction grating") on either a photographic film or throughout the volume of a photosensitive block, rather than as a concentration (or point) of photosensitive material. The data storage capability of the recording medium is not reduced by storing data by spatially dispersed elements because the elements are allowed to overlap. Indeed, the storage capacity is in fact increased because a single film defect does not obliterate any data value but merely reduces the accuracy of retrieval of all stored data values with elements containing the defect. Each such element can modulate a suitable diffracted optical beam. It was found that the "diffraction efficiency" of these elements was easily controllable to form visible images or could act multiplicatively on the diffracted beam in both phase and amplitude. The phase of the diffracted beam is detetmined by the spatial displacement of the bars of the dispersed grating and thus little affected by any one optical imperfection of the medium. An excellent account of holography has been given by R. J. Collier, IEEE Spectrum, Vol. 3, p. 67, July 1966.
In an article in IEEE Spectrum, Vol. 1, p. 101, Oct. 1964, L. J. Cutrona shows how the transparencies and masks of earlier coherent optical computers can be replaced with holograms to allow linear computations with negative and complex numbers. The transmission of the earlier transparency is replaced by the diffraction of a hologram such that a value of a numerical quantity is represented by a diffraction efficiency of a hologram. In particular, Cutrona cites B. A. Vander Lugt, IEEE Trans. Information Theory, Vol. IT-10, No. 2, p. 139, Apr. 1964, who shows how complex spatial filters (a special type of linear operation) can be used in pattern recognition by means of an electronic threshold device. Recognition is indicated by a sufficiently bright spot (high discriminant function value) in the pictorial output of the holographic device. Cutrona (op. cit.) also suggests that a non-linear capability could be attained in coherent optical computers by replication of input transparencies and their insertion at two or more parts of the device to produce an auto-correlation function.
In the simplest holographic concept, the recording medium is very thin film. Thin holograms look like photographic transparencies except that in incoherent white light they appear a uniform gray since the image points or data points are dispersed over the entire film. A suitable coherent light beam is needed to bring out the encoded image or access the data values. An entirely different effect is produced when a substantially thicker photosensitive medium is used. Then the diffraction efficiency can be so large that most of the incident light is diffracted back in the general direction of the source as by a mirror. Collier (op. cit.) explains how thick holograms can act as mirrors. Such holograms can be quite selective in their diffracting capability allowing some beams to pass while strongly diffracting others. Even ordinary commercial fine grain photographic film has a thick enough emulsion to exhibit the effects of thick holograms as explained by E. N. Leith, et al., Applied Optics. Vol. 5, No. 8, p. 1303, August 1966.
Even thicker holograms have been prepared in solid crystalline media and their applications to data storage have been described by P. J. van Heerden, Applied Optics, Vol. 2, No. 4, p. 393, April 1963. Van Heerden shows how a three-dimensional diffraction grating consisting of equally spaced planes of optically altered material may extend throughout the volume of the crystal and diffract an incident plane wave if and only if the plane wave makes a certain angle (the so-called Bragg angle) to the diffraction grating planes. Even though the crystal may contain very many such overlapping diffraction elements, they can be selectively accessed or read out by adjusting the angle of the incident wave. Van Heerden shows how an extremely large data storage capacity may be obtained in this way. Even though van Heerden does not use the term hologram, it is clear from other references such as Collier (op. cit.) or Leith, et al. (op. cit.), that van Heerden's device would be considered holographic in current terminology.
Both coherent and incoherent optical computers described above may be said to be passive, in that once the input optical illumination is supplied, no additional energy is required to form the products and sums used in the output. The many output values are formed simultaneously and essentially instantaneously by the passage of the optical rays and beams through the computer.
This discussion of prior art optical computers has described incoherent optical computers which form non-linear polynomial functions of input data recorded on a single transparency. Also, coherent optical computers have been described which form linear functions of the input data and make use of the high data storage capacity of holograms and their capability of storing negative and complex numbers. When applied to the calculation of linear discriminant functions, this type of computing device has proven effective in pattern recognition. It should be noted that improvements in pattern recognition capability can be expected if non-linear polynomial discriminant functions are used as shown by D. F. Specht, IEEE Trans. Electronic Computers, Vol. EC-16, No. 3, p. 308, June 1967. Also, polynomials are well known to be useful for approximating non-algebraic functions (e.g., truncated Taylor series), but negative coefficients are needed in these approximations.